In mathematics, a polynomial sequence, i.e., a sequence of polynomials indexed by { 0, 1, 2, 3, ... } in which the index of each polynomial equals its degree, is said to be of binomial type if it satisfies the sequence of identities
Many such sequences exist. The set of all such sequences forms a Lie group under the operation of umbral composition, explained below. Every sequence of binomial type may be expressed in terms of the Bell polynomials. Every sequence of binomial type is a Sheffer sequence (but most Sheffer sequences are not of binomial type). Polynomial sequences put on firm footing the vague 19th century notions of umbral calculus.
Read more about Binomial Type: Examples, Characterization By Delta Operators, Characterization By Bell Polynomials, Characterization By A Convolution Identity, Characterization By Generating Functions, Umbral Composition of Polynomial Sequences, Cumulants and Moments, Applications
Famous quotes containing the word type:
“We have two kinds of “conference.” One is that to which the office boy refers when he tells the applicant for a job that Mr. Blevitch is “in conference.” This means that Mr. Blevitch is in good health and reading the paper, but otherwise unoccupied. The other type of “conference” is bona fide in so far as it implies that three or four men are talking together in one room, and don’t want to be disturbed.”
—Robert Benchley (1889–1945)